Hi, What is the best way to estimate the SNR of a sinusoidal signal in white noise using an FFT? For the best SNR estimate, is it better to do one long FFT or to break up into smaller FFTs to average the noise power? Also does windowing have an effect on the measured SNR? Thanks, Rizwan

# SNR estimation using a windowed FFT

Started by ●July 13, 2007

Reply by ●July 14, 20072007-07-14

On Jul 13, 7:44 pm, reah...@gmail.com wrote:> Hi, > > What is the best way to estimate the SNR of a sinusoidal signal in > white noise using an FFT? For the best SNR estimate, is it better to > do one long FFT or to break up into smaller FFTs to average the noise > power? Also does windowing have an effect on the measured SNR? > > Thanks, > > RizwanIs the frequency of the sinusoid known? For your estimation problem, recall that due to Parseval's relations, power estimate of white noise can be done either in frequency or in time. The issue is to isolating the effect of the sinusoid. Julius

Reply by ●July 15, 20072007-07-15

On Jul 14, 5:17 pm, julius <juli...@gmail.com> wrote:> On Jul 13, 7:44 pm, reah...@gmail.com wrote: > > > Hi, > > > What is the best way to estimate the SNR of a sinusoidal signal in > > white noise using an FFT? For the best SNR estimate, is it better to > > do one long FFT or to break up into smaller FFTs to average the noise > > power? Also does windowing have an effect on the measured SNR? > > > Thanks, > > > Rizwan > > Is the frequency of the sinusoid known? > > For your estimation problem, recall that due to > Parseval's relations, power estimate of white > noise can be done either in frequency or in > time. The issue is to isolating the effect of > the sinusoid. > > JuliusYes, the frequency is known (the experiment is injecting a tone to measure receiver Noise figure). What I am worried about is the effect of the windowing on the noise / signal power. Without windowing, noise power of the FFT output rises linearly with N while signal power rises as N^2 (so SNR goes up by N). However, with windowing, noise power should go up by sum from n = 0 to N-1 of w[n]^2 while signal power goes up by ( sum from n = 0 to N-1 of w[n] ) ^2 for a hamming window, the resulting SNR is ~1.75 dB less than for a rectangular window. Is this correct or am I missing something here? Thanks, Rizwan

Reply by ●July 17, 20072007-07-17

On Jul 15, 12:42 am, reah...@gmail.com wrote:> On Jul 14, 5:17 pm, julius <juli...@gmail.com> wrote: > > > > > On Jul 13, 7:44 pm, reah...@gmail.com wrote: > > > > Hi, > > > > What is the best way to estimate the SNR of a sinusoidal signal in > > > white noise using an FFT? For the best SNR estimate, is it better to > > > do one long FFT or to break up into smaller FFTs to average the noise > > > power? Also does windowing have an effect on the measured SNR? > > > > Thanks, > > > > Rizwan > > > Is the frequency of the sinusoid known? > > > For your estimation problem, recall that due to > > Parseval's relations, power estimate of white > > noise can be done either in frequency or in > > time. The issue is to isolating the effect of > > the sinusoid. > > > Julius > > Yes, the frequency is known (the experiment is injecting a tone to > measure receiver Noise figure). What I am worried about is the effect > of the windowing on the noise / signal power. Without windowing, > noise power of the FFT output rises linearly with N while signal power > rises as N^2 (so SNR goes up by N). However, with windowing, > > noise power should go up by sum from n = 0 to N-1 of w[n]^2 > > while signal power goes up by ( sum from n = 0 to N-1 of w[n] ) ^2 > > for a hamming window, the resulting SNR is ~1.75 dB less than for a > rectangular window. Is this correct or am I missing something here? > > Thanks, > > RizwanFor a pure sinusoidal signal the amount of loss will depend on if the tone falls exactly on FFT bin or not. You will suffer the coherent loss when the tone fall exactly on an FFT bin, and the scalloping loss when it is exactly half way. You may want to look at a Flat Top type window - see the B&K tech. manuals. You still have sidelobes and other considerations. Cheers, David

Reply by ●July 17, 20072007-07-17

On Jul 14, 9:42 pm, reah...@gmail.com wrote:> On Jul 14, 5:17 pm, julius <juli...@gmail.com> wrote: > > > > > On Jul 13, 7:44 pm, reah...@gmail.com wrote: > > > > Hi, > > > > What is the best way to estimate the SNR of a sinusoidal signal in > > > white noise using an FFT? For the best SNR estimate, is it better to > > > do one long FFT or to break up into smaller FFTs to average the noise > > > power? Also does windowing have an effect on the measured SNR? > > > > Thanks, > > > > Rizwan > > > Is the frequency of the sinusoid known? > > > For your estimation problem, recall that due to > > Parseval's relations, power estimate of white > > noise can be done either in frequency or in > > time. The issue is to isolating the effect of > > the sinusoid. > > > Julius > > Yes, the frequency is known (the experiment is injecting a tone to > measure receiver Noise figure). What I am worried about is the effect > of the windowing on the noise / signal power. Without windowing, > noise power of the FFT output rises linearly with N while signal power > rises as N^2 (so SNR goes up by N). However, with windowing, > > noise power should go up by sum from n = 0 to N-1 of w[n]^2 > > while signal power goes up by ( sum from n = 0 to N-1 of w[n] ) ^2 > > for a hamming window, the resulting SNR is ~1.75 dB less than for a > rectangular window. Is this correct or am I missing something here?The second moment of a Hamming window is less than that of the same width rectangular window. This is related to why a Hamming window (or any of the "hump shaped" windows) appears to act like a shorter or narrower rectangular window in terms of signal power and noise power, which as you found, results in a lower SNR. However, if your sinusoidal signal is not centered in an fft bin, then it is much easier to subtract out most of the signal from the combined S+N fft result given a Hamming windowed fft, since the transform of a Hamming window is much more localized than a complex sinc. IMHO. YMMV. -- rhn A.T nicholson d.0.t C-o-M